Let W be the subspace of R 4 generated by the vectors (1, −2, 5, −3),(2, 3, 1, −4) and (3, 8, −3, −5). find the basis and the dimension of W and the extend the basis of W to a basis of the whole space R 4 .

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

what are you trying to solve here

step-by-step explanation: